Based on conventional Gerchberg-Saxton (GS) algorithm, transport of intensity equation (TIE) method and accelerated angular spectrum iterative algorithm are introduced to put forward a kind of more accurate and rapid phase recovery algorithm: accelerated angular spectrum iterative algorithm for two-dimensional (2D) phase retrieval from TIE. The intensity distribution of three planes, e.g., an incident plane and two emergent planes, is employed to retrieve the initial phase by TIE and then retrieve the phase of incident optical field by accelerated angular spectrum iterative algorithm. The simulation result shows that this algorithm can retrieve the phase distribution of an arbitrary 2D incident optical field in high accuracy. Through numerical simulation, this algorithm is proved in 2D image phase recovery process to be more accurate and faster and its noise immunityis stronger. In the recovery phase control range, the iteration tends to be stable after 40 steps, and the mean square (RMS) error can be controlled in the order of magnitude of 10-6.